Werner Ogiers - TNT Belgium
December, 2008

Triggered by the incredibly stupid mistake I made in the text of the CanRong digital VTF scale, I set out to investigate the effects of tonearm geometry and mass distribution on the measurement of VTF at a point not perfectly coincident with the stylus' actual operating position, as happens when using scales that are thicker (or thinner, should that be possible) than an LP record. Indeed, what is the point of scales seemingly accurate to 0.001 g when, depending on the arm being used, they can introduce a systematic measurement error of up to 0.3g!

Consider the above schematic representation of a tonearm with a low-slung counterweight. The upper diagram holds for an arm floating in balance, i.e. before VTF is set. In this state its center of gravity lies on a vertical line through the bearing pivot or fulcrum. Gravity pulls down on this center of gravity, its force represented by the red arrow, but no motion ensues as this force has no moment or torque around the fulcrum. (Note that the vertical reaction force in the fulcrum is not drawn, to keep the diagram uncluttered.)

Now if the arm is lifted at its business end to a height above its normal playing field, the arm's center of gravity swings to the left and up. Due to the horizontal displacement of the center of gravity, the gravitional force now develops a torque around the pivot that tries to turn the arm counterclockwise. If the arm is held stationary in this position then this implies a vertical reaction force at the stylus tip: suddenly there appears to be a phantom VTF component, a component that is absent when the arm returns to its horizontal position.

As a result, measuring the actual VTF at the stylus tip at any height above the record surface will result in an over-reading of VTF, an error. The amount of error depends heavily on the actual mass distribution and layout of the tonearm in use. Let's have a look at a number or archetypes:

I made a number of virtual tonearms, all with the same mass and primary dimensions (233 mm tube length, 16 g tube mass, 100 g counterweight mass, 50 mm stub length, 20 g stub mass, 10 g cartridge mass) but differing in parts layout and features, and set them up for an effective vertical tracking force of 2g at the LP surface. The picture above shows these arms, with each time a red dot indicating the position of the arm's center of gravity as it would appear when playing records.

I then lifted (virtually of course) the arms at the stylus ends by 5 millimeters, and re-assessed the tracking force as measured in this new position. I also had a look at the displacement of the centers of gravity. Here are the results (all figures apply of course only to the precise masses and dimensions as used in the model, and not to any real-life tonearm):

Arm type	COG horizontal position (mm)	COG vertical position (mm)	VTF reading in elevated position (g)
Generic	-2.7	0	1.999
Generic with low-slung weight	-2.7	-6.8	2.120
Generic with downward VTF spring	0	0	2.000
RB-300 with upward VTF spring	-4.8	0	1.998
SME IV	-3.2	-1.4	2.018
Uni-pivot	-3.2	-21	2.285

The first arm type is the generic arm where all masses lie more or less on a horizontal line through the pivot, with the VTF applied statically, i.e. by moving the counterweight. The Rega RB-250 belongs to this categoty, as do the many arms on seventies and eighties Japanese consumer turntables. With a set VTF the arms center of gravity (COG) lies left of the fulcrum, but at the same height. This position makes the setup almost immune to misreadings of VTF when the arm is lifted.

The second arm copies the first type but now with a counterweight that sits in a considerably lowered position relative to the fulcrum, as would be encountered with e.g. the many available upgrade counterweights that are available for the Rega arms. This configuration puts the COG to the left and below the fulcrum. As a result VTF varies considerably with stylus height, with a serious overreading of 0.12g at 5mm height.

The third arm is a variant of the first arm, but with VTF applied dynamically: first the arm is brought into static balance with the counterweight, then a spring applies a counterclockwise torque to set VTF. The arm is always in balance, its COG located exactly at the pivot. There is no sensitivity at all of VTF with respect to the stylus height. Arms like these were often used on Duals, and perhaps you remember that manufacturer's show trick where a playing turntable revolved in a gyroscope-like contraption?

The fourth arm is like the third, but now with a spring applying a clockwise torque. The only arms of this type are, as far as I know, the Regas above and including the RB-300. The COG is again to the left of and in line with the pivot, only more to the left than with the first arm. The sensitivity of VTF to height is almost zero.

Then we have an arm with the pivot in line with the stylus, and a counterweight slightly below that, as exemplified in the SME IV and 309 series. The center of gravity sits somewhat below the fulcrum and as a consequence the arm shows some VTF sensitivity, enough to worry about when trying to set the force to within 0.01g.

The last arm is a typical uni-pivot with a high pivot and a very low counterweight. The latter is required to balance the pivot, but it also moves the COG so low that it gives a very large sensitivity of VTF to stylus height, in fact so much that this effect should be calculated into the set-up when using any type of scales that don't measure exactly at the LP surface.

As said, the simulated setup was for a VTF of 2 g and a stylus elevation of 5 mm above LP level. The latter is a bit extreme, not too many record-dedicated scales with exhibit such platform height (then again, many a non-audio scale will be far worse!). As the effect on VTF is near-linear at low elevations it is easy to scale down to any required height. E.g. the CanRong I tested earlier with its 3 mm high platform would measure the uni-pivot arm at 2+ 3 * (2.285-2) / 5 = 2.17 g.